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As with past natural disasters, the Sandy aid bill is not offset with spending cuts, meaning the aid adds to the deficit. The lone exception is an offset provision requiring that $3.4 billion for Army Corps of Engineers projects to protect against future storms be covered by an equal amount of unspecified spending cuts in other programs before next October.

The Senate on Monday rejected, 35-62, an attempt by Sen. Mike Lee, R-Utah, to amend the final package Monday with a provision to cut federal programs across the board by one-half of 1 percent through 2021 as a way to prevent the disaster aid from swelling the U.S. debt.

While the bill passed by the Senate carries a $50.5 billion price tag, it could trim 5 percent or so if across-the-board spending cuts are allowed to take place on March 1 as scheduled under current law.

The cuts, known as a sequester, are punishment for the failure of a congressional deficit "supercommittee" to follow up a 2011 budget pact with additional deficit curbs. The cuts would apply equally to every account in the measure.

As of Monday, FEMA said it spent $3.3 billion in disaster relief money for shelter, restoring power and other immediate needs arising from the storm.

New York, New Jersey, Connecticut, West Virginia, Virginia, Maryland, New Hampshire, Ohio, Delaware, Rhode Island, Pennsylvania, Massachusetts and the District of Columbia have shared that money.